AQR Section 18 Exercise 44

Recall that the heights of WNBA players are Normally distributed with a mean of 72 in. and a standard deviationof 2 in., and that NBA players’ heights have a mean of 79 in. and a standard deviation of 3 in. Obviously, NBA players are taller on average than WNBA players. However, it is possible to find a WNBA player that is taller than an NBA player. Likewise, it is possible to find an NBA player shorter than a WNBA player. Suppose a player (NBA or WNBA) player is chosen at random. You are only given the height of the chosen player. How likely is it that you mistake a WNBA player for an NBA player based only on the player's height?